Question

Use the distributive property to express each sum with the GCF factored out.

A) a(b+c)
B) a² +b²
C) a³ −b³
D) a+b+c

Answer 1

To factor out the GCF using the distributive property, you can distribute the GCF to each term inside the parentheses (if possible). If there is no GCF, the expression remains unchanged.

Step-by-step explanation:

A) To factor out the greatest common factor (GCF) from the expression a(b+c), you can distribute the GCF to both terms inside the parentheses. This gives you the expression ab + ac.

B) In the expression a² + b², there is no common factor to factor out. Therefore, the expression cannot be simplified any further using the distributive property.

C) To factor out the GCF from the expression a³ - b³, you can rewrite it as (a - b)(a² + ab + b²).

D) In the expression a + b + c, again there is no common factor to factor out. So, it remains as it is.